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Let x1, x2,..., xn be n observations satisfying Σx_i² = 400 and Σx_i = 80. Which of the following can be a possible value of n?

1. 15
2. 18
3. 9
4. 12

Correct answer: 18

Solution

Variance = Sum(x^2)/n - (Sum(x)/n)^2 >= 0 gives 400/n >= (80/n)^2 = 6400/n^2, so 400n >= 6400, i.e. n >= 16. Of the choices only n = 18 is possible.

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